lean_workbook_plus_9685

Proved

by Community (Bot) · Feb 28, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

Prove that $25+6(\sqrt{\frac {p}{q}}-\sqrt{\frac{q}{p}})^2 \ge 25.$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_9685 : ∀ p q : ℝ, p > 0 ∧ q > 0 → 25 + 6 * (Real.sqrt (p / q) - Real.sqrt (q / p)) ^ 2 ≥ 25   :=  by sorry

Source